Modeling and prediction for movies

Setup

Load packages

library(ggplot2)
library(dplyr)
library(statsr)
library(GGally)
library(knitr)
library(gridExtra)

Load data

Make sure your data and R Markdown files are in the same directory. When loaded your data file will be called movies. Delete this note when before you submit your work.

load("movies.Rdata")

---

Part 1: Data

What is this data about?

• The dataset contains a list of randomly sampled movies from the IMDB and Rotten Tomatoe movie databases.

• It contains information about both audience and critic scores about how much they like/dislike movies. As well as other variables associated with the movie.

• The dataset contains 651 rows and 32 variables.

• The codebook can be viewed from this link: Code Book

Sampling:

• Random Sampling was used in the selection of the movies from the IMDB and Rotten Tomatoe databases.

Generalizability and Association vs Causation

Generalizability :

• The survey uses data from the Rotten Tomatoes and IMDB databases.

• These are some of the biggest databases in the world, that has data on a huge repository of movies from around the world.

• However, on closer inspection. The data about the movies in the sample contain only English language movies.

Answer :

• So we can safely say that the sample data is generalizable only to English language movies from the IMDB and Rotten Tomato database.

Causality :

• The data is Associative at the moment.

• However, controlled random assignment of new movies to any model generated, can be used to establish causal relationships between response and explanatory variables.

Answer :

• The data is Associative at the moment.

• However ,there is a possibilty of drawing conclusions on causality only after conducting many simulations on generated models to figure out there is strong evidence of causality between the response and explanatory variables used to create the model.

---

Part 2: Research question

What are the best predictor variables to create an accurate model to predict an IMDB score ?

• Real life modelling involves,looking at lots of variables from different sources and piecing them together to make a robust model that can predict an acurate outcome at a specified confidence interval.

• I am interested in creating a predictor with a 95% confidence interval to predict the IMDB score of a movie, based on various predictor variables.

• I am planning to create the most efficient parsimonious model, which can explain most of the variability in the IMDB ratings.

• In order to achieve this , I will be using a forward selection approach, with emphasis on getting the best adjusted R-squared value.

---

Part 3: Exploratory data analysis

Step1 :

We begin by having an overview of the model:

str(movies)

## Classes 'tbl_df', 'tbl' and 'data.frame':    651 obs. of  32 variables:
##  $ title           : chr  "Filly Brown" "The Dish" "Waiting for Guffman" "The Age of Innocence" ...
##  $ title_type      : Factor w/ 3 levels "Documentary",..: 2 2 2 2 2 1 2 2 1 2 ...
##  $ genre           : Factor w/ 11 levels "Action & Adventure",..: 6 6 4 6 7 5 6 6 5 6 ...
##  $ runtime         : num  80 101 84 139 90 78 142 93 88 119 ...
##  $ mpaa_rating     : Factor w/ 6 levels "G","NC-17","PG",..: 5 4 5 3 5 6 4 5 6 6 ...
##  $ studio          : Factor w/ 211 levels "20th Century Fox",..: 91 202 167 34 13 163 147 118 88 84 ...
##  $ thtr_rel_year   : num  2013 2001 1996 1993 2004 ...
##  $ thtr_rel_month  : num  4 3 8 10 9 1 1 11 9 3 ...
##  $ thtr_rel_day    : num  19 14 21 1 10 15 1 8 7 2 ...
##  $ dvd_rel_year    : num  2013 2001 2001 2001 2005 ...
##  $ dvd_rel_month   : num  7 8 8 11 4 4 2 3 1 8 ...
##  $ dvd_rel_day     : num  30 28 21 6 19 20 18 2 21 14 ...
##  $ imdb_rating     : num  5.5 7.3 7.6 7.2 5.1 7.8 7.2 5.5 7.5 6.6 ...
##  $ imdb_num_votes  : int  899 12285 22381 35096 2386 333 5016 2272 880 12496 ...
##  $ critics_rating  : Factor w/ 3 levels "Certified Fresh",..: 3 1 1 1 3 2 3 3 2 1 ...
##  $ critics_score   : num  45 96 91 80 33 91 57 17 90 83 ...
##  $ audience_rating : Factor w/ 2 levels "Spilled","Upright": 2 2 2 2 1 2 2 1 2 2 ...
##  $ audience_score  : num  73 81 91 76 27 86 76 47 89 66 ...
##  $ best_pic_nom    : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ best_pic_win    : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ best_actor_win  : Factor w/ 2 levels "no","yes": 1 1 1 2 1 1 1 2 1 1 ...
##  $ best_actress_win: Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ best_dir_win    : Factor w/ 2 levels "no","yes": 1 1 1 2 1 1 1 1 1 1 ...
##  $ top200_box      : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ director        : chr  "Michael D. Olmos" "Rob Sitch" "Christopher Guest" "Martin Scorsese" ...
##  $ actor1          : chr  "Gina Rodriguez" "Sam Neill" "Christopher Guest" "Daniel Day-Lewis" ...
##  $ actor2          : chr  "Jenni Rivera" "Kevin Harrington" "Catherine O'Hara" "Michelle Pfeiffer" ...
##  $ actor3          : chr  "Lou Diamond Phillips" "Patrick Warburton" "Parker Posey" "Winona Ryder" ...
##  $ actor4          : chr  "Emilio Rivera" "Tom Long" "Eugene Levy" "Richard E. Grant" ...
##  $ actor5          : chr  "Joseph Julian Soria" "Genevieve Mooy" "Bob Balaban" "Alec McCowen" ...
##  $ imdb_url        : chr  "http://www.imdb.com/title/tt1869425/" "http://www.imdb.com/title/tt0205873/" "http://www.imdb.com/title/tt0118111/" "http://www.imdb.com/title/tt0106226/" ...
##  $ rt_url          : chr  "//www.rottentomatoes.com/m/filly_brown_2012/" "//www.rottentomatoes.com/m/dish/" "//www.rottentomatoes.com/m/waiting_for_guffman/" "//www.rottentomatoes.com/m/age_of_innocence/" ...

Result:

• We see there are 10 numeric variables in the dataset:

• title,actor1-actor5 , imdb_url, rt_url are 9 character variables.

• there are 12 factor variables in the dataset.

• there is 1 integer variable imdb_num_votes.

Step2 :

Let us now plot a ggpairs plot of all the numeric variables in our dataset.

m1 <- movies%>%select(c(runtime,thtr_rel_year,thtr_rel_month,thtr_rel_day,dvd_rel_year,dvd_rel_month,dvd_rel_day,imdb_rating,imdb_num_votes,critics_score,audience_score))

ggpairs(data = m1)

ANOVA

AnoV <- aov(imdb_rating~imdb_num_votes+critics_score+audience_score+runtime+thtr_rel_year+thtr_rel_month+thtr_rel_day+dvd_rel_year+dvd_rel_month+dvd_rel_day, data = m1)
summary(AnoV)

##                 Df Sum Sq Mean Sq  F value   Pr(>F)    
## imdb_num_votes   1   82.8    82.8  368.243  < 2e-16 ***
## critics_score    1  370.2   370.2 1647.482  < 2e-16 ***
## audience_score   1  139.1   139.1  619.149  < 2e-16 ***
## runtime          1    4.6     4.6   20.292 7.92e-06 ***
## thtr_rel_year    1    0.5     0.5    2.247    0.134    
## thtr_rel_month   1    0.3     0.3    1.124    0.289    
## thtr_rel_day     1    0.0     0.0    0.059    0.808    
## dvd_rel_year     1    0.0     0.0    0.048    0.827    
## dvd_rel_month    1    0.5     0.5    2.018    0.156    
## dvd_rel_day      1    0.3     0.3    1.327    0.250    
## Residuals      631  141.8     0.2                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 9 observations deleted due to missingness

Multiple R-squared: 0.8083808

Adjusted R-squared: 0.805344

• We observe from ANOVA: critics_score, audience_score, imdb_num_votes, runtime. Contribute maximum to the variability, due to ther high values.

• We will rebuild a model with only these 4, to see what the R values look like.

AnoV <- aov(imdb_rating~imdb_num_votes+critics_score+audience_score+runtime, data = m1)
summary(AnoV)

##                 Df Sum Sq Mean Sq F value   Pr(>F)    
## imdb_num_votes   1   84.3    84.3  372.74  < 2e-16 ***
## critics_score    1  386.0   386.0 1707.26  < 2e-16 ***
## audience_score   1  143.1   143.1  633.04  < 2e-16 ***
## runtime          1    4.6     4.6   20.33 7.74e-06 ***
## Residuals      645  145.8     0.2                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 1 observation deleted due to missingness

Multiple R-squared: 0.8090797

Adjusted R-squared: 0.8078957

Result: Why did we pick only these 4 numeric variables

• We see that this parsimonious model has a better overall adjusted R-squared

• Therefore, these 4 numeric variables will be analyzed in depth, to build out model.

• Also these 4 numeric variables have the highest correlation coefficients, which indicated they have a more linear relationship. The other numeric variables can be dropped from consideration since they do not have strong linear relationsips.

• I am NOT taking the critics_score and audience_score collinearity. Because there has been times when critics and audiences have diverging scores. So even though the correlation seems high, based on experience. I am not going to use collineartiy to drop one of them. Besides there must be some really important information that seems to superceded the collinearity condition, as the adjusted_R squared value has actually gone up substantially.

Step3 :

plot IMDB rating against the 11 factor variables(excluding studio) to see if we can learn something:

m2 <- movies%>%select(c(imdb_rating,title_type,genre,mpaa_rating,critics_rating,audience_rating,best_pic_nom,best_pic_win,best_actor_win,best_actress_win,best_dir_win,top200_box))

ggpairs(data = m2)

Result:

• Looking at the first row, we can see that most categorical variables exhibit a high degree of variance against the imdb_rating. This is something interesting that needs to be noted. the 3 that seem to have the least variance are: best_actor_win, best_actress_win, best_director_win.

---

ANOVA and adjusted-R-Squared: imdb_rating vs title_type

AnoV <- aov(imdb_rating~title_type, data = m2)
summary(AnoV)

##              Df Sum Sq Mean Sq F value Pr(>F)    
## title_type    2   83.7   41.84    39.8 <2e-16 ***
## Residuals   648  681.2    1.05                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Result:

Multiple R-squared: 0.1094114

Adjusted R-squared: 0.1066627

Note adjusted R-squared has not dropped significantly, this seems like a good candidate for our model

---

ANOVA and adjusted-R-Squared: imdb_rating vs genre

AnoV <- aov(imdb_rating~genre, data = m2)
summary(AnoV)

##              Df Sum Sq Mean Sq F value Pr(>F)    
## genre        10  174.5  17.446   18.91 <2e-16 ***
## Residuals   640  590.4   0.922                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Result:

Multiple R-squared: 0.2281009

Adjusted R-squared: 0.21604

Note adjusted R-squared has not dropped significantly, this seems like a good candidate for our model

---

ANOVA and adjusted-R-Squared: imdb_rating vs mpaa_rating

AnoV <- aov(imdb_rating~mpaa_rating, data = m2)
summary(AnoV)

##              Df Sum Sq Mean Sq F value   Pr(>F)    
## mpaa_rating   5   55.8  11.157   10.15 2.26e-09 ***
## Residuals   645  709.1   1.099                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Result:

Multiple R-squared: 0.0729363

Adjusted R-squared: 0.0657497

Note mpaa_rating seems to have a verly low R-squared and an even lower adjusted R-squared. We may ignore this while buiilding the model.

---

ANOVA and adjusted-R-Squared: imdb_rating vs critics_rating

AnoV <- aov(imdb_rating~critics_rating, data = m2)
summary(AnoV)

##                 Df Sum Sq Mean Sq F value Pr(>F)    
## critics_rating   2  309.3   154.7     220 <2e-16 ***
## Residuals      648  455.5     0.7                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Result:

Multiple R-squared: 0.4044055

Adjusted R-squared: 0.4025673

Note adjusted R-squared has not dropped significantly, this seems like a good candidate for our model

---

ANOVA and adjusted-R-Squared: imdb_rating vs audience_rating

AnoV <- aov(imdb_rating~audience_rating, data = m2)
summary(AnoV)

##                  Df Sum Sq Mean Sq F value Pr(>F)    
## audience_rating   1  369.6   369.6     607 <2e-16 ***
## Residuals       649  395.2     0.6                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Result:

Multiple R-squared: 0.4832746

Adjusted R-squared: 0.4824785

Note adjusted R-squared has not dropped significantly, this seems like a good candidate for our model

---

ANOVA and adjusted-R-Squared: imdb_rating vs best_pic_nom

AnoV <- aov(imdb_rating~best_pic_nom, data = m2)
summary(AnoV)

##               Df Sum Sq Mean Sq F value   Pr(>F)    
## best_pic_nom   1   36.0   35.97   32.03 2.28e-08 ***
## Residuals    649  728.9    1.12                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

lm2_1 <- lm(imdb_rating~best_pic_nom, data = m2)
summary(lm2_1)

## 
## Call:
## lm(formula = imdb_rating ~ best_pic_nom, data = m2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5491 -0.5491  0.0509  0.7509  2.0509 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      6.44913    0.04225  152.62  < 2e-16 ***
## best_pic_nomyes  1.30087    0.22986    5.66 2.28e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.06 on 649 degrees of freedom
## Multiple R-squared:  0.04703,    Adjusted R-squared:  0.04556 
## F-statistic: 32.03 on 1 and 649 DF,  p-value: 2.279e-08

Note adjusted R-squared has not dropped significantly, this seems like a good candidate for our model

---

ANOVA and adjusted-R-Squared: imdb_rating vs best_pic_win

AnoV <- aov(imdb_rating~best_pic_win, data = m2)
summary(AnoV)

##               Df Sum Sq Mean Sq F value   Pr(>F)    
## best_pic_win   1   14.0  14.006   12.11 0.000536 ***
## Residuals    649  750.8   1.157                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

lm2_1 <- lm(imdb_rating~best_pic_win, data = m2)
summary(lm2_1)

## 
## Call:
## lm(formula = imdb_rating ~ best_pic_win, data = m2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5778 -0.5778  0.1222  0.8222  2.0222 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      6.47780    0.04238 152.834  < 2e-16 ***
## best_pic_winyes  1.42220    0.40874   3.479 0.000536 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.076 on 649 degrees of freedom
## Multiple R-squared:  0.01831,    Adjusted R-squared:  0.0168 
## F-statistic: 12.11 on 1 and 649 DF,  p-value: 0.000536

Note This seems like a decent candidate, but might be dropped as adjusted R-squared is quite small

---

ANOVA and adjusted-R-Squared: imdb_rating vs best_actor_win

AnoV <- aov(imdb_rating~best_actor_win, data = m2)
summary(AnoV)

##                 Df Sum Sq Mean Sq F value Pr(>F)  
## best_actor_win   1    3.2   3.189   2.717 0.0998 .
## Residuals      649  761.7   1.174                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

lm2_1 <- lm(imdb_rating~best_actor_win, data = m2)
summary(lm2_1)

## 
## Call:
## lm(formula = imdb_rating ~ best_actor_win, data = m2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5645 -0.5645  0.0355  0.8355  2.3355 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        6.46452    0.04586 140.961   <2e-16 ***
## best_actor_winyes  0.20000    0.12134   1.648   0.0998 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.083 on 649 degrees of freedom
## Multiple R-squared:  0.004169,   Adjusted R-squared:  0.002635 
## F-statistic: 2.717 on 1 and 649 DF,  p-value: 0.09977

Note adjusted R-squared is too small to be of significance, this looks to be definitely dropped. This corresponds to the lack of noticable variance in the box-plots.

---

ANOVA and adjusted-R-Squared: imdb_rating vs best_actress_win

AnoV <- aov(imdb_rating~best_actress_win, data = m2)
summary(AnoV)

##                   Df Sum Sq Mean Sq F value Pr(>F)  
## best_actress_win   1    3.9   3.897   3.324 0.0687 .
## Residuals        649  760.9   1.172                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

lm2_1 <- lm(imdb_rating~best_actress_win, data = m2)
summary(lm2_1)

## 
## Call:
## lm(formula = imdb_rating ~ best_actress_win, data = m2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5658 -0.5658  0.1342  0.8342  2.2875 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           6.4658     0.0450 143.684   <2e-16 ***
## best_actress_winyes   0.2467     0.1353   1.823   0.0687 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.083 on 649 degrees of freedom
## Multiple R-squared:  0.005096,   Adjusted R-squared:  0.003563 
## F-statistic: 3.324 on 1 and 649 DF,  p-value: 0.06874

Note adjusted R-squared is too small to be of any value, we will ignore this while building the model

---

ANOVA and adjusted-R-Squared: imdb_rating vs best_dir_win

AnoV <- aov(imdb_rating~best_dir_win, data = m2)
summary(AnoV)

##               Df Sum Sq Mean Sq F value   Pr(>F)    
## best_dir_win   1   13.9  13.865   11.98 0.000572 ***
## Residuals    649  751.0   1.157                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

lm2_1 <- lm(imdb_rating~best_dir_win, data = m2)
summary(lm2_1)

## 
## Call:
## lm(formula = imdb_rating ~ best_dir_win, data = m2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5543 -0.5543  0.0457  0.7519  2.0457 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      6.45428    0.04363 147.948  < 2e-16 ***
## best_dir_winyes  0.58758    0.16974   3.462 0.000572 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.076 on 649 degrees of freedom
## Multiple R-squared:  0.01813,    Adjusted R-squared:  0.01662 
## F-statistic: 11.98 on 1 and 649 DF,  p-value: 0.0005722

Note adjusted R-squared is really small, we will be dropping this while building the model

---

ANOVA and adjusted-R-Squared: imdb_rating vs top200_box

AnoV <- aov(imdb_rating~top200_box, data = m2)
summary(AnoV)

##              Df Sum Sq Mean Sq F value Pr(>F)  
## top200_box    1    6.4   6.425   5.499 0.0193 *
## Residuals   649  758.4   1.169                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

lm2_1 <- lm(imdb_rating~top200_box, data = m2)
summary(lm2_1)

## 
## Call:
## lm(formula = imdb_rating ~ top200_box, data = m2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5778 -0.5778  0.1222  0.8222  2.5222 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    6.47783    0.04286 151.122   <2e-16 ***
## top200_boxyes  0.66217    0.28239   2.345   0.0193 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.081 on 649 degrees of freedom
## Multiple R-squared:  0.008401,   Adjusted R-squared:  0.006873 
## F-statistic: 5.499 on 1 and 649 DF,  p-value: 0.01933

Note adjusted R-squared os really small. We won’t be including this in our model

---

Step4 :

Now we can look at the relationship between IMDB_ratings and studios next:

m3 <- movies%>%select(c(imdb_rating,studio))

#m4 <- movies%>%select(c(imdb_rating,title))
ggplot(data = m3,aes(x = studio, y = imdb_rating))+geom_boxplot()+coord_flip()

##ggplot(data = m4[1:10,], aes(x = title, y = imdb_rating))+geom_boxplot()

Let us do an ANOVA to check if there is any relationship, as well as check the adjusted R-squared via a linear model.

AnoV <- aov(imdb_rating~studio, data = m3)
summary(AnoV)

##              Df Sum Sq Mean Sq F value  Pr(>F)   
## studio      210  306.5   1.460   1.406 0.00173 **
## Residuals   432  448.6   1.038                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 8 observations deleted due to missingness

lm4 <- lm(imdb_rating~studio, data = m3)
summary(lm4)$r.squared

## [1] 0.4059134

summary(lm4)$adj.r.squared

## [1] 0.1171212

• boxplot of imdb_rating versus studio shows an interesting variation among the different studios. Certain studios show a skewed distribution with hign medians, with long left or right skewes, certain other studions have a median high imdb_rating, compared to the rest. This box plot has lots of interesting information. And can be it’s own topic of research.

• NOTE The difference between R-squared of: 0.4059 and adjusted R-squared: 0.1171. Which is very steep. This seems to indicate that adding studio to our model, might actually reduce the overall adjusted-R squared of our model. And it also seems to show that studio is not necessarily a good predictor variable.

Result:

• We see a high degree of variance between the studios with respect to the IMDB_ratings. So it looks like studios might have a strong influence in the imdb_ratings.

• We need to keep this in mind when we build our model.

I am interested if the title of a movie, has any influence on audience, affecting the imdb_rating of a movie.

• imdb_url and rt_url, offer no real value, as they merely are locations in the internet of where information about the movies is found.

Step5 :

Influence on lead actor on IMDB_ratings:

• Another factor of interest, is to see if actors have any influence on movie quality thereby influencing the IMDB_rating

• Lead actors can sometimes have a major influence on ratings of movies. I will be exploring the relationship between the actor1 variable and the IMDB_ratings next.

m5 <- movies%>%select(c(imdb_rating,actor1))
ggplot(data = m5,aes(x = actor1, y = imdb_rating))+geom_boxplot()+coord_flip()

Let us do a more formal check with an ANOVA analysis as well as fit to a linear model just to make sure. Before we get the R squared value.

AnoV <- aov(imdb_rating~actor1, data = m5)
summary(AnoV)

##              Df Sum Sq Mean Sq F value   Pr(>F)    
## actor1      484  635.9  1.3138   1.706 3.71e-05 ***
## Residuals   164  126.3  0.7703                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 2 observations deleted due to missingness

lm5 <- lm(imdb_rating~actor1, data = m5)
summary(lm5)$r.squared

## [1] 0.8342664

summary(lm5)$adj.r.squared

## [1] 0.3451501

• the boxplot presents lots of interesting information on lead actors and their movies.

• It says quite a bit about what kind of movies that the actors seem to fall into. for example: Adam Sandler although famous seems to be starring in movies with really low IMDB ratings. Arnold Schwazneggar seems to star in movies with overall higher median IMDB rating.

• Although we see variance, can it be completely attributed to just the actor or to other factors such as the director.

• Nevertheless, this is an interestng variable to consider too.

• NOTE One really interesting trend is the difference between R-squared of: 0.8342 and adjusted R-squared: 0.3452. From this we see that adding in more actors into the predictors actually results in a higher penality. So from this it looks like, actor1 is not necessarily a good predictor variable

---

Part 4: Modeling

• We will now begin creating the model by using the forward selection R-squared approach.

• We will add one predictor variable at a time, and check if the R-squared value increases or decreases. Predictor variables that lower R-squared will be dropped.

• Our strategy for adding the predictor variables will follow this strategy:-

• First we will be adding the numeric predictor variables, we will add predictors that result in increased adjustd R-squared. We will then run tests on them to make sure that they satisfy the conditions needed to be added in a MLR model. If they fail to satisfy the conditions, we will remove them from the model.

• We will follow the same approach and add in the categorical variables.

Let us list out their R-squared and Adjusted R-square values:

kable(RsquaredSummary)

predictorVariable	VariableType	rsquared	adjrsquared
audience_rating	Categorical	0.4832746	0.4824785
critics_rating	Categorical	0.4044055	0.4025673
actor1	Categorical	0.8342664	0.3451501
genre	Categorical	0.2281009	0.2160400
studio	Categorical	0.4059134	0.1171212
title_type	Categorical	0.1094114	0.1066627
mpaa_rating	Categorical	0.0729363	0.0657497
best_pic_nom	Categorical	0.0470320	0.0455636
best_pic_win	Categorical	0.0183129	0.0168003
best_dir_win	Categorical	0.0181285	0.0166156
top200_box	Categorical	0.0084011	0.0068732
best_actress_win	Categorical	0.0050955	0.0035625
best_actor_win	Categorical	0.0041689	0.0026345
audience_score	Numeric	0.7479917	0.7476034
critics_score	Numeric	0.5852793	0.5846403
imdb_num_votes	Numeric	0.1096620	0.1082901
runtime	Numeric	0.0719530	0.0705208

Section 1: Build model with numeric variables

• We will be considering the following numeric_variables, since they have the largest correleation coefficients: audience_score, critics_score, imdb_num_votes, runtime

model <- lm(imdb_rating~audience_score+critics_score, data = movies)

summary(model)$r.squared

## [1] 0.7962356

summary(model)$adj.r.squared

## [1] 0.7956067

# p1 <- ggplot(data = model, aes(x = audience_score, y = .resid))+geom_point()+geom_hline(yintercept=0, linetype="dashed", color = "red")
# 
# 
# p2 <- ggplot(data = model, aes(x = .resid)) + geom_histogram() + xlab("Residuals")
# #QQ-plot
# p2_1 <- ggplot(data = model, aes(sample = .resid)) + stat_qq()+stat_qq_line(size=1.25, color="red")
# 
# p3 <- ggplot(data = model, aes(x = .fitted, y = .resid))+geom_point()+geom_hline(yintercept=0, linetype="dashed", color = "red")
# p3_1 <- ggplot(data = model, aes(x = abs(.fitted), y = .resid))+geom_point()+geom_hline(yintercept=0, linetype="dashed", color = "red")
# 
# 
# print(p1)
# print(p2)
# print(p2_1)
# print(p3)
# print(p3_1)


#hist(model$residuals)
#qqnorm(model$residuals)
#qqline(model$residuals)
#plot(model$residuals~model$fitted)+abline(h = 0)
#plot(abs(model$residuals)~model$fitted)+abline(h = 0)
#plot(model$residuals)+abline(h = 0)
#modelSummary <- data.frame( modelPredVar = modelPredVar,modelRsquare = modelRsquare ,modeladjRsquare = modeladjRsquare)

summary(model)

## 
## Call:
## lm(formula = imdb_rating ~ audience_score + critics_score, data = movies)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.51964 -0.19767  0.03466  0.30671  1.22691 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.647241   0.062471   58.38   <2e-16 ***
## audience_score 0.034703   0.001340   25.90   <2e-16 ***
## critics_score  0.011816   0.000954   12.39   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4904 on 648 degrees of freedom
## Multiple R-squared:  0.7962, Adjusted R-squared:  0.7956 
## F-statistic:  1266 on 2 and 648 DF,  p-value: < 2.2e-16

Let us plot all the numeric variables to check for costant variability vs residuals

plot(model$residuals~movies$audience_score)+abline(h = 0)

## integer(0)

plot(model$residuals~movies$critics_score)+abline(h = 0)

## integer(0)

plot(model$residuals~movies$imdb_num_votes)+abline(h = 0)

## integer(0)

plot(model$residuals~movies$runtime)+abline(h = 0)

## integer(0)

• audience_score is constatnly variable , so we keep it.

• critics_score is constantly variable so we keep it.

• imdb_num_votes is not constantly variable so we drop it.

• runtime is not constantly variable so we drop it.

model <- lm(imdb_rating~audience_score, data = movies)

After adding: audience_score

the R-squared: 0.7479917

the adjusted R-squared: 0.7476034

model <- lm(imdb_rating~audience_score+critics_score, data = movies)

After adding: critics_score

the R-squared: 0.7962356

the adjusted R-squared: 0.7956067

The adjusted R-squared has increased, so critics score is a useful predictor variable, along with audience_score

Section 2: Build model with categorical variables

audience_rating

model <- lm(imdb_rating~audience_score+critics_score+audience_rating, data = movies)
hist(model$residuals, main = "Normally distrbuted Residuals")

qqnorm(model$residuals)
qqline(model$residuals)

plot(model$residuals~model$fitted,main = "Residual vs fitted")+abline(h = 0)

## integer(0)

plot(abs(model$residuals)~model$fitted,main = "Residual vs fitted")+abline(h = 0)

## integer(0)

plot(model$residuals,main = "Check for time-dependent variations")+abline(h = 0)

## integer(0)

• From the plots: audience_rating shows: Constant variability. Nearly Normal residuals.

After adding: audience_rating

the R-squared: 0.8045298

the adjusted R-squared: 0.8036235

The adjusted- R squared increased so we keep this predictor

critics_rating

model <- lm(imdb_rating~audience_score+critics_score+audience_rating+critics_rating, data = movies)
hist(model$residuals, main = "Normally distrbuted Residuals")

qqnorm(model$residuals)
qqline(model$residuals)

plot(model$residuals~model$fitted,main = "Residual vs fitted")+abline(h = 0)

## integer(0)

plot(abs(model$residuals)~model$fitted,main = "Residual vs fitted")+abline(h = 0)

## integer(0)

plot(model$residuals,main = "Check for time-dependent variations")+abline(h = 0)

## integer(0)

• From the plots: audience_rating shows: Constant variability. Nearly Normal residuals.

After adding: critics_rating

the R-squared: 0.808689

the adjusted R-squared: 0.8072059

The adjusted- R squared increased so we keep this predictor

genre

model <- lm(imdb_rating~audience_score+critics_score+audience_rating+critics_rating+genre, data = movies)
hist(model$residuals, main = "Normally distrbuted Residuals")

qqnorm(model$residuals)
qqline(model$residuals)

plot(model$residuals~model$fitted,main = "Residual vs fitted")+abline(h = 0)

## integer(0)

plot(abs(model$residuals)~model$fitted,main = "Residual vs fitted")+abline(h = 0)

## integer(0)

plot(model$residuals,main = "Check for time-dependent variations")+abline(h = 0)

## integer(0)

• From the plots: audience_rating shows: Constant variability. Nearly Normal residuals.

After adding: genre

the R-squared: 0.8240338

the adjusted R-squared: 0.8198771

The adjusted- R squared increased so we keep this predictor

best_pic_win

model <- lm(imdb_rating~audience_score+critics_score+audience_rating+critics_rating+genre+best_pic_win, data = movies)
hist(model$residuals, main = "Normally distrbuted Residuals")

qqnorm(model$residuals)
qqline(model$residuals)

plot(model$residuals~model$fitted,main = "Residual vs fitted")+abline(h = 0)

## integer(0)

plot(abs(model$residuals)~model$fitted,main = "Residual vs fitted")+abline(h = 0)

## integer(0)

plot(model$residuals,main = "Check for time-dependent variations")+abline(h = 0)

## integer(0)

• From the plots: audience_rating shows: Constant variability. Nearly Normal residuals.

After adding: best_pic_win

the R-squared: 0.8244864

the adjusted R-squared: 0.820057

The adjusted- R squared increased so we keep this predictor

• The remaining categorical variables were ignored as they caused a decrease in adjuster - r squared.

• Also studio and actor1 are not really categorical variables, as they do not have categories , but just a whole bunch of actor and studio names.

• There fore in our model they are not used.

---

Part 5: Prediction

Wonder Woman(2017)

#Wonder Woman rating
newprof <- data.frame(audience_score = 87 ,critics_score = 93 ,audience_rating = "Upright" ,critics_rating = "Certified Fresh",genre = "Action & Adventure",best_pic_win = "no")
p1 <- predict(model, newprof, interval = "prediction", level = 0.95)
kable(p1)

fit	lwr	upr
7.705417	6.79029	8.620543

predicted value: 7.7054169

original IMDB rating: 7.4

prediction off by(percentage): 3.0541693

ORIGINAL IMDB VALUE falls inside PREDICTED Confidence interval of 95%

Star Wars: The Last Jedi (2018)

#SW The Last Jedi
newprof <- data.frame(audience_score = 43 ,critics_score = 91 ,audience_rating = "Spilled" ,critics_rating = "Certified Fresh",genre = "Action & Adventure",best_pic_win = "no")
predict(model, newprof, interval = "prediction", level = 0.95)

##        fit      lwr      upr
## 1 6.191144 5.271704 7.110583

p1 <- predict(model, newprof, interval = "prediction", level = 0.95)
kable(p1)

fit	lwr	upr
6.191144	5.271704	7.110583

predicted value: 6.1911436

original IMDB rating: 7.0

prediction off by(percentage): -8.0885645

ORIGINAL IMDB VALUE falls inside PREDICTED Confidence interval of 95%

Star Wars: The Rise of Skywalker (2019)

#SW The rise of skywalker
newprof <- data.frame(audience_score = 86 ,critics_score = 52 ,audience_rating = "Upright" ,critics_rating = "Rotten",genre = "Action & Adventure",best_pic_win = "no")
predict(model, newprof, interval = "prediction", level = 0.95)

##        fit      lwr      upr
## 1 7.329901 6.414344 8.245458

p1 <- predict(model, newprof, interval = "prediction", level = 0.95)
kable(p1)

fit	lwr	upr
7.329901	6.414344	8.245458

predicted value: 7.3299008

original IMDB rating: 6.7

prediction off by(percentage): 6.2990085

ORIGINAL IMDB VALUE falls inside PREDICTED Confidence interval of 95%

James Bond 007: Casino Royale 007

#James Bond 007: Casino Royale 007
newprof <- data.frame(audience_score = 89 ,critics_score = 95 ,audience_rating = "Upright" ,critics_rating = "Certified Fresh",genre = "Action & Adventure",best_pic_win = "no")
predict(model, newprof, interval = "prediction", level = 0.95)

##        fit      lwr      upr
## 1 7.819608 6.904118 8.735097

p1 <- predict(model, newprof, interval = "prediction", level = 0.95)
kable(p1)

fit	lwr	upr
7.819608	6.904119	8.735097

predicted value: 7.8196079

original IMDB rating: 8

prediction off by(percentage): -1.8039209

ORIGINAL IMDB VALUE falls inside PREDICTED Confidence interval of 95%

---

Part 6: Conclusion

• Our model is really accurate in the 95% confidence interval . It is able to predicted IMDB rating values accurately such that they fall into this confidence interval.

• The mean loss of precision of our model is: 6.3480396

• Our model is well designed as it takes into account, diveregence of opinion between Critics and Audiences.`

• This is a robust well designed model.